Introduction to Probability

Probability I – Edexcel GCSE (1MA1): Foundation Tier

In this course, Dr Sunil Chhita (Durham University) explores probability, covering topics P1-P5 in the Pearson Edexcel GCSE (9-1) Mathematics (1MA1) Specification for Foundation Tier. In the first mini-lecture, we give an introduction to probability and discuss important definitions, notation, and applications. In the second mini-lecture, we explore how to represent data using frequency tables and frequency trees (Topic P1). In the third mini-lecture, we define randomness, fairness, and equally likely events, and learn how to calculate the expected outcomes of multiple future experiments (Topic P2). In the fourth mini-lecture, we explore the differences between relative expected frequencies and theoretical probabilities (Topic P3). In the fifth mini-lecture, we discuss exhaustive sets of outcomes and mutually exclusive events, while learning how the probabilities of these types of events sum to one (Topic P4). In the sixth mini-lecture, we learn about theoretical probability distributions and how experimental probability gets closer to theoretical probability with an increase of trials (Topic P5).

Introduction to Probability

In this mini-lecture, we give an introduction to probability. We think about: (i) the definition of probability: the study of randomness and chance; (ii) applications of probability in machine learning, biology, statistics, and physics; (iii) a motivating example from genetics where we see how probability can be used to predict alleles of offspring; (iv) how probability is used to estimate or calculate the likelihood of an event occurring; (v) examples of calculating probability and their corresponding chances using a sliding scale: flipping a fair coin, rolling a fair six-sided die; (vi) the equation describing the probability of an outcome: probability of an outcome (event) = number of ways the outcome occurs / the number of possible outcomes; (vii) the notation used to describe the probability of an event: P[Event]; (viii) examples of calculating probabilities; and (ix) a non-examinable remark on probability from two philosophical perspectives: the approach made by ‘Frequentists’ and the approach made by ‘Subjectives/Bayesians.’